Covariance adjustments for the analysis of randomized field experiments

It has become common practice to analyze randomized experiments using linear regression with covariates. Improved precision of treatment effect estimates is the usual motivation. In a series of important articles, David Freedman showed that this approach can be badly flawed. Recent work by Winston Lin offers partial remedies, but important problems remain.

In this article, we address those problems through a reformulation of the Neyman causal model. We provide a practical estimator and valid standard errors for the average treatment effect. Proper generalizations to well-defined populations can follow.

In most applications, the use of covariates to improve precision is not worth the trouble.